近年來，隨著數據傳輸和應用的發展，正交多重存取( OMA ) 技術不能支持不斷增加的用戶和設備。對更高頻譜效率，大規模連接和更低延遲的要求給現有的移動網絡帶來了巨大壓力。面對這些挑戰，非正交多重存取 ( NOMA ) 可以在5G和無線網絡中實現大規模連接，以非正交方式將資源單位分配給用戶，從而允許多個用戶共享相同的資源單位，提高了系統的頻譜效率，並滿足了對行動網路和物聯網（IoT）不斷增長的需求。本文所使用的稀疏碼多重存取 ( SCMA )為一種典型的NOMA技術。它通過SCMA編碼過程將多維調變和低密度擴頻序列（LDS）相結合，把二進制輸入訊號直接映射為用戶碼本中的稀疏碼字，來獲得多維星座的整形增益( shaping gain )。
但是SCMA對於碼本設計的方法存在多維星座設計複雜度高和擴頻矩陣的選擇等難以確定的問題。因此，本文將碼本設計的步驟拆分為幾個部份，分別進行探討和研究，將複雜的設計明確化，並且利用多維星座的關鍵性能指標（KPI）來選擇最佳設計參數。針對不同通道條件、不同使用者和通道數量的情況下，提出一個在各個步驟中都具有最佳效能的碼本。基本思想是在平均功率固定的情況下，最大化星座點的最小歐幾里得距離和最小乘積距離，並且選擇最大周長值的因子圖，從而獲得比其他論文碼本更好的BER性能。

In recent years, with the development of data transmission and applications, OMA technique cannot support a huge number of users and devices. The requirements for large-scale connectivity, lower latency, and higher spectrum efficiency have put tremendous pressure on mobile networks. In the face of these challenges, non-orthogonal multiple access (NOMA) enables massive connectivity in 5G and wireless networks. NOMA allocates resource elements to users in a non-orthogonal manner, allowing multiple users to share the same resource elements. It improves the spectral efficiency of the system, meeting the needs of the ever-growing demand for mobile Internet and the Internet-of-Things (IoT). Sparse code multiple access (SCMA) is a typical NOMA technology. It combines multi-dimensional modulation and low density spreading (LDS) through SCMA encoding process. It mapped the binary input bits to the sparse code words in the user codebook, and obtained the shaping gain of the multi-dimensional constellation.
However, for the SCMA codebook design method, there are problems that are difficult to determine, such as the high complexity of designing a multi-dimensional constellation and the selection of a spreading matrix. Therefore, the paper divides the steps of codebook design into several parts for discussion and research respectively. Explain the complex design clearly, and use the key performance indicators (KPI) of the multi-dimensional constellation to select the best design parameters. I propose a codebook with the best performance in each step, for different channel conditions, different numbers of users and channels. The basic idea is to maximize the minimum Euclidean distance and the minimum product distance of the constellation point when the average power is fixed, and to select the factor graph of the maximum girth value to obtain better BER performance than other papers codebooks.

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